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Ch 3.2: Fundamental Solutions of Linear Homogeneous Equations

Ch 3.2: Fundamental Solutions of Linear Homogeneous Equations. Let p , q be continuous functions on an interval I = ( ? , ? ), which could be infinite. For any function y that is twice differentiable on I , define the differential operator L by

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Generating Functions

Generating Functions. The Moments of Y. We have referred to E(Y) and E(Y 2 ) as the first and second moments of Y, respectively. In general, E(Y k ) is the k th moment of Y. Consider the polynomial where the moments of Y are incorporated into the coefficients. Moment Generating Function.

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Generalized Derangements

Generalized Derangements. Anthony Fraticelli Missouri State University REU July 30, 2009 Advisor: Dr. Les Reid. Overview. In this presentation we will address the following: Introductory definitions Classic derangements k -derangements Exponential generating functions Limits

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Ch 3.3: Linear Independence and the Wronskian

Ch 3.3: Linear Independence and the Wronskian. Two functions f and g are linearly dependent if there exist constants c 1 and c 2 , not both zero, such that for all t in I . Note that this reduces to determining whether f and g are multiples of each other.

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388 views • 10 slides

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Whose coefficients - PowerPoint PPT Presentation

Ch 3.2: Fundamental Solutions of Linear Homogeneous Equations

Generating Functions

Generalized Derangements

Ch 3.3: Linear Independence and the Wronskian